Effects of Mix Components on Fracture Properties of Seawater Volcanic Scoria Aggregate Concrete

The fracture mechanism and macro-properties of SVSAC were studied using a novel test system combined with numerical simulations, which included three-point bending beam tests, the digital image correlation (DIC) technique, scanning electron microscopy (SEM), and ABAQUS analyses. In total, 9 groups and 36 specimens were fabricated by considering two critical parameters: initial notch-to-depth ratios (a0/h) and concrete mix components (seawater and volcanic scoria coarse aggregate (VSCA)). Changes in fracture parameters, such as the load-crack mouth opening displacement curve (P-CMOD), load-crack tip opening displacement curve (P-CTOD), and fracture energy (Gf), were obtained. The typical double-K fracture parameters (i.e., initial fracture toughness (KICini) and unstable fracture toughness (KICun)) and tension-softening (σ-CTOD) curve were analyzed. The test results showed that the initial cracking load (Pini), Gf, and characteristic length (Lch) of the SVSAC increased with decreasing a0/h. Compared with the ordinary concrete (OC) specimen, the P-CMOD and P-CTOD curves of the specimen changed after using seawater and VSCA. The evolution of the crack propagation length was obtained through the DIC technique, indicating cracks appeared earlier and the fracture properties of specimen decreased after using VSCA. Generally, the KICun and KICini of SVSAC were 36.17% and 8.55% lower than those of the OC specimen, respectively, whereas the effects of a0/h were negligible. The reductions in Pini, Gf, and Lch of the specimen using VSCA were 10.94%, 32.66%, and 60.39%, respectively; however, seawater efficiently decreased the negative effect of VSCA on the fracture before the cracking width approached 0.1 mm. Furthermore, the effects of specimen characteristics on the fracture mechanism were also studied through numerical simulations, indicating the size of the beam changed the fracture toughness. Finally, theoretical models of the double-K fracture toughness and the σ-CTOD relations were proposed, which could prompt their application in marine structures.


Introduction
The construction of marine islands and reefs has become an urgent issue owing to the implementation of a strategy for building a powerful marine country, particularly for China's large economic need [1].Seawater volcanic scoria aggregate concrete (SVSAC) is an advantageous option for marine construction owing to its advantages such as locally available material and huge deposits, which can shorten the construction period and reduce the cost.For SVSAC, the coarse aggregates, mixed water, and fine aggregates are volcanic scoria coarse aggregate (VSCA), seawater (SW), and sea sand (SS), respectively [2].Volcanic scoria aggregates (VSAs) are characterized by a porous structure, low elastic modulus, porosity, and light weight [3,4].SS and SW contain numerous chloride ions (Cl − ) and sulphates (SO 4  2− ).Thus, the properties of SVSAC are more complex than those of ordinary concrete (OC) and require further investigation.
The mix components of SVSAC (VSCA, SW, and SS) are the main causes of their complex behaviors.In general, VSCA is obtained from volcanic scoria which is an important kind of pyroclastic material and has the basic composition of basalt [5].The volcanic scoria aggregates have been extensively adopted in past construction [6][7][8][9].The ancient Roman architects started to adopt volcanic scoria aggregates to fabricate mortars or 'Roman concrete' with special characteristics from the first century before Christ (e.g., Pantheon (Rome), the monuments of imperial age in Rome) [10,11].The influence of VSCA on concrete properties (e.g., strength, ductility, and fire resistance) has been studied through several analyses [12][13][14].The test results indicated that the lightweight and porous structure of VSCA decreased the concrete density, resulting in a lower deformability compared to that of the OC by approximately 15-30%.Hossian [15] revealed that VSCA had a detrimental influence on the workability of concrete, and the slump of concrete was acceptable by preparing VSCA under saturated-surface dry conditions [16].VSCA can also be used to develop a series of concrete grades that exhibit sufficient desirable strength and acceptable durability in the structural range.The results indicated that after substituting VSCA for gravel, the concrete compressive and tensile strengths decreased by approximately by 8.35-40% and 2-30%, respectively [17,18], and the ratio of tensile strength to compressive strength of concrete with VSCA was 0.08-0.11.The increase in concrete strength can reach 50% when river sand (RS) is replaced with volcanic scoria fine aggregate (VSFA), owing to the desirable particle size distribution and granular properties of VSFA [19].The elastic and rupture modulus of specimen adopting VSCA were 10-21 GPa and 2.7-4.8MPa, respectively [20], and the variation in the concrete's Poisson's ratio (0.19-0.21) was negligible.In general, the stress-strain relationship of concrete adopting VSCA under uniaxial compression is different from that of OC [21,22].SW and SS also significantly affected the properties of the concrete.The addition of SS improved the slump and fluidity of concrete, whereas a high shell content significantly affected the workability of the concrete.The carbonation, Cl − penetration, and freezing resistances of concrete adopting SW and SS were improved compared to those of OC [23][24][25].For the underwater structures using Roman concrete, SW caused an immediate chemical reaction, and hydrated silicates and calcium aluminosilicates were formed and C-S-H phases were created, which ensured the connection of all ingredients [7].Xiao [26], Huang et al. [27], and Sariman et al. [28] studied the compressive strength of seawater sea sand concrete at different ages and revealed that its strength developed rapidly during the early ages owing to the high Cl − content, which accelerated the hydration reaction of cement.However, the development of strength was delayed after 28 days, and the ductility of concrete with SW and SS decreased slightly [29].Huang et al. [2] investigated the mechanical properties of concrete by simultaneously adopting the VSCA, SW, and SS under axial compression.It was observed that the specimen failed suddenly, and its deformability and elastic modulus were approximately 20.5% and 31.7%inferior to those of OC, respectively.Based on the above findings, the workability, strength, and durability of SVSAC met the construction requirements.However, the cracking of SVSAC was different from that of OC, which reduced the deformability and ductility of the specimen.
Fracture investigations can reveal the principle of material cracking (initiation and propagation of cracks), which can improve the behavior of structures.Several research works [30,31] obtained the evolution of the crack propagation length based on digital image correlation (DIC) technology and verified the reliability of DIC.Gui et al. [32] systematically studied the fracture properties of concrete containing SW and SS.The fracture toughness of the specimens increased with the maximum aggregate size.Zang et al. [33] and Zhou et al. [34] reported that concrete mixed with SW and SS, replacing freshwater and RS, can improve the unstable fracture toughness and fracture energy and decrease its brittleness.Zhou et al. [35] proposed that coral concrete is more brittle, less ductile, and prone to cracking, whereas seawater immersion curing can improve its hydration degree of coral concrete and densify the interfacial transition zone (ITZ) between the coral coarse aggregate and cement matrix.However, to the best of our knowledge, few studies have focused on the fracture properties of concrete using VSCA, and the coupled effects of SW, SS, and VSCA on the fracture of concrete have not yet been studied.Further tests and theoretical analyses are required to confirm this hypothesis.Thus, a systematic investigation on the fracture properties of SVSAC was undertaken in this study through a novel test system combined with numerical simulations, which included three-point bending beam tests, the digital image correlation (DIC) technique, scanning electron microscopy (SEM), and ABAQUS analyses.The macro fracture performance and mechanism of SVSAC are investigated by this test system.

Raw Materials
The main parameters in this study were the initial notch-to-depth ratios (a 0 /h: 0.2, 0.3, and 0.4) and the concrete mix components (SW, SS, and VSCA).Considering the effects of the mix components, three types of concrete were used in the test, i.e., OC, SVSAC, and volcanic scoria aggregate concrete (VSAC).Notably, the mixed water and fine and coarse aggregates of the VSAC were fresh water (FW), RS, and VSCA, respectively.
The mixing water in the test included SW and freshwater, and the fine aggregates consisted of SS and RS (Figure 1).To determine the effects of coarse aggregates on fracture performance, two types of coarse aggregates were considered: VSCA and gravel (Figure 2).P.O 42.5 ordinary cement and an HSC polycarboxylic acid high-performance water-reducing agent were used to fabricate the specimens.The basic properties and compositions of the aggregates are listed in Table 1.
Materials 2024, 17, x FOR PEER REVIEW 3 of 27 prone to cracking, whereas seawater immersion curing can improve its hydration degree of coral concrete and densify the interfacial transition zone (ITZ) between the coral coarse aggregate and cement matrix.However, to the best of our knowledge, few studies have focused on the fracture properties of concrete using VSCA, and the coupled effects of SW, SS, and VSCA on the fracture of concrete have not yet been studied.Further tests and theoretical analyses are required to confirm this hypothesis.Thus, a systematic investigation on the fracture properties of SVSAC was undertaken in this study through a novel test system combined with numerical simulations, which included three-point bending beam tests, the digital image correlation (DIC) technique, scanning electron microscopy (SEM), and ABAQUS analyses.The macro fracture performance and mechanism of SVSAC are investigated by this test system.

Raw Materials
The main parameters in this study were the initial notch-to-depth ratios (a0/h: 0.2, 0.3, and 0.4) and the concrete mix components (SW, SS, and VSCA).Considering the effects of the mix components, three types of concrete were used in the test, i.e., OC, SVSAC, and volcanic scoria aggregate concrete (VSAC).Notably, the mixed water and fine and coarse aggregates of the VSAC were fresh water (FW), RS, and VSCA, respectively.
The mixing water in the test included SW and freshwater, and the fine aggregates consisted of SS and RS (Figure 1).To determine the effects of coarse aggregates on fracture performance, two types of coarse aggregates were considered: VSCA and gravel (Figure 2).P.O 42.5 ordinary cement and an HSC polycarboxylic acid high-performance waterreducing agent were used to fabricate the specimens.The basic properties and compositions of the aggregates are listed in Table 1.Compared with gravel (Table 1), the ω a and CR of VSCA increased by 1134.17% and 210.95%, respectively; however, its ρ b and ρ a were 54.62% and 36.41%lower, respectively.The lightweight and porous structure of volcanic scoria changed the properties of VSCA (Figure 3).SS had a higher α, while its CL was acceptable.SW was obtained from Lingshan Bay, Qingdao, China.The main chemical compositions of SW were Cl − (19.83 g/L), Na + (9.22 g/L), SO 42− (2.31 g/L), Mg 2+ (1.12 g/L), and Ca 2+ (0.34 g/L), etc.

Concrete Mix
The target concrete strength adopted was C30 because of its wide application in practical engineering [36,37].Three types of concrete were prepared: OC, VSAC, and SVSAC,

Concrete Mix
The target concrete strength adopted was C30 because of its wide application in practical engineering [36,37].Three types of concrete were prepared: OC, VSAC, and SVSAC, to systematically study the effects of the concrete mix components on the fracture properties of the SVSAC specimen.The details of the concrete mix were determined through preliminary tests, as listed in Table 2.The mix proportions of VSAC and SVSAC were different from those of OC owing to the properties of the aggregates.The effects of the concrete mix components (SW, SS, and VSCA) and initial notch-todepth ratios (a 0 /h = 0.2, 0.3, and 0.4) on the fracture properties of SVSAC were investigated using 9 groups and 36 three-point bending beams.According to RILEM50-FMC [38] and the related code, the specific size of the beam was maintained at 200 × 100 × 1190 mm 3 (width × height × length), and the initial crack width was 3 mm.
The specimens were named according to the following rules (Table 3): concrete type (OC, VSAC, and SVSAC), a 0 /h (0.2, 0.3, and 0.4).Taking SVSAC-0.2 as an example, "SVSAC" and "0.2" denote seawater volcanic scoria aggregate concrete and a 0.2 initial notch-to-depth ratio, respectively.The specimens were fabricated as follows.First, the concrete mixture was filled into a test mold and vibrated uniformly.Second, prefabricated cracks were obtained by carefully removing the prebuilt steel plates (3 mm thickness) after the initial setting of the concrete (3 h).Third, the mold was removed after 24 h, and the specimens were cured under standard conditions for 28 d (temperature: 23 ± 2 • C, humidity: 95 ± 3%).The actual beam specimens are shown in Figure 4.The effects of the concrete mix components (SW, SS, and VSCA) and initial notch-to depth ratios (a0/h = 0.2, 0.3, and 0.4) on the fracture properties of SVSAC were investigate using 9 groups and 36 three-point bending beams.According to RILEM50-FMC [38] an the related code, the specific size of the beam was maintained at 200 × 100 × 1190 mm (width × height × length), and the initial crack width was 3 mm.

OC
The specimens were named according to the following rules (Table 3): concrete typ (OC, VSAC, and SVSAC), a0/h (0.2, 0.3, and 0.4).Taking SVSAC-0.2 as an example "SVSAC" and "0.2" denote seawater volcanic scoria aggregate concrete and a 0.2 initia notch-to-depth ratio, respectively.The specimens were fabricated as follows.First, the concrete mixture was filled int a test mold and vibrated uniformly.Second, prefabricated cracks were obtained by care fully removing the prebuilt steel plates (3 mm thickness) after the initial setting of th concrete (3 h).Third, the mold was removed after 24 h, and the specimens were cure under standard conditions for 28 d (temperature: 23 ± 2 °C, humidity: 95 ± 3%).The actua beam specimens are shown in Figure 4.

Loading Setup and Program
The loading setup for the fracture studies included three parts: an MTS-SANS (MTS Corporation, Eden Prairie, MN, USA) (30 kN) electronic universal testing system, a measuring system (i.e., clip gauges, strain gauges, and linear variable differential transformers (LVDTs)), and a computer system, as shown in Figure 5. Clip gauges with a maximum range of 50 mm were placed at the bottom and tip ends of the notch to measure the crack mouth opening displacement (CMOD) and crack tip opening displacement (CTOD) during the test.The LVDTs (50 mm) were arranged at the midspan and ends of the beam to obtain the deflection.Furthermore, four strain gauges were symmetrically attached to the pre-notched tip on both sides of the beam to determine the crack initiation (Figure 5).camera to reduce errors.
In addition, a vacuum control system, a signal detection and image display system, and an electronic optical system were utilized in conjunction, collectively comprising an Apreo S HiVac scanning electron microscope (Thermo Fisher Scientific, Shanghai, China) (SEM) system (Figure 6b) to analyze the microstructure of concrete and SVSAC.The dimensions of the specimens were consistently maintained at 5 mm × 5 mm × 2 mm.The digital image correlation (DIC) technique was adapted to measure the full-field surface displacement of the beam and obtain the crack propagation and characteristics such as the crack opening displacement (COD) and crack propagation length (l l ).An area of 200 × 100 mm 2 above the notch was prepared using the DIC technique (Figure 6a).Images of the specimen during the test were captured and analyzed using the DIC technique (aperture value of f /6.3, exposure time of 1/13 s, and image acquisition frequency of 0.5 Hz).It should be noted that the specimen was positioned perpendicularly to the industrial camera to reduce errors.Displacement control was used during the test, and the loading rate was maintained at 0.02 mm/min with a data acquisition frequency of 30 Hz.A 1 kN load was applied to the beam to ensure normal operation of the loading system before the actual test.Furthermore, digital images of the deformed specimens were captured using an industrial camera every 2 s to record the related information.

Failure Phenomenon
The failure of the SVSAC three-point bending beam was similar to that of the OC and VSAC specimens.The initial cracking of the beam first appeared at the tip of the notch In addition, a vacuum control system, a signal detection and image display system, and an electronic optical system were utilized in conjunction, collectively comprising an Apreo S HiVac scanning electron microscope (Thermo Fisher Scientific, Shanghai, China) (SEM) system (Figure 6b) to analyze the microstructure of concrete and SVSAC.The dimensions of the specimens were consistently maintained at 5 mm × 5 mm × 2 mm.
Displacement control was used during the test, and the loading rate was maintained at 0.02 mm/min with a data acquisition frequency of 30 Hz.A 1 kN load was applied to the beam to ensure normal operation of the loading system before the actual test.Furthermore, digital images of the deformed specimens were captured using an industrial camera every 2 s to record the related information.

Failure Pattern
The failure of the SVSAC three-point bending beam was similar to that of the OC and VSAC specimens.The initial cracking of the beam first appeared at the tip of the notch when the vertical load (P) reached approximately 60-70% of peak load (P max ).The number of cracks increased with increasing P. The cracks propagated approximately parallel to the loading direction (Figure 7).Deformation and cracks in the beam became evident when P approached P max .After the peak point, P decreased rapidly, and cracks crossed the entire section of the beam.The specimens failed suddenly.at 0.02 mm/min with a data acquisition frequency of 30 Hz.A 1 kN load was applied to the beam to ensure normal operation of the loading system before the actual test.Furthermore, digital images of the deformed specimens were captured using an industrial camera every 2 s to record the related information.

Failure Pattern
The failure of the SVSAC three-point bending beam was similar to that of the OC and VSAC specimens.The initial cracking of the beam first appeared at the tip of the notch when the vertical load (P) reached approximately 60-70% of peak load (Pmax).The number of cracks increased with increasing P. The cracks propagated approximately parallel to the loading direction (Figure 7).Deformation and cracks in the beam became evident when P approached Pmax.After the peak point, P decreased rapidly, and cracks crossed the entire section of the beam.The specimens failed suddenly.
The typical fracture surfaces of the beams are shown in Figure 8.Compared to OC, the aggregates of VSAC and SVSAC were almost damaged, and their fracture surfaces were smooth, irrespective of a0/h (Figure 8).This can be attributed to the cracks that can easily cross the porous and lightweight VSCA.SS and SW had negligible effects on the fracture surface, and the failure pattern of VSAC was similar to that of SVSAC.The typical fracture surfaces of the beams are shown in Figure 8.Compared to OC, the aggregates of VSAC and SVSAC were almost damaged, and their fracture surfaces were smooth, irrespective of a 0 /h (Figure 8).This can be attributed to the cracks that can easily cross the porous and lightweight VSCA.SS and SW had negligible effects on the fracture surface, and the failure pattern of VSAC was similar to that of SVSAC.

Crack Propagation and Characteristics
The crack propagation during the fracture process of the concrete specimens in this study was recorded using the DIC technique (Figures 9-11).The displacement jump map obtained by DIC was also adopted to reveal the development of crack characteristics (COD and ll) (Figures 12-14).The calculation method is described in Refs.[39,40].The crack characteristics were negligible during the early loading stage.

Crack Propagation and Characteristics
The crack propagation during the fracture process of the concrete specimens in this study was recorded using the DIC technique (Figures 9-11).The displacement jump map obtained by DIC was also adopted to reveal the development of crack characteristics (COD and l l ) (Figures 12-14).The calculation method is described in Refs.[39,40].The crack characteristics were negligible during the early loading stage.

Crack Propagation and Characteristics
The crack propagation during the fracture process of the concrete specimens in this study was recorded using the DIC technique (Figures 9-11).The displacement jump map obtained by DIC was also adopted to reveal the development of crack characteristics (COD and ll) (Figures 12-14).The calculation method is described in Refs.[39,40].The crack characteristics were negligible during the early loading stage.

Crack Propagation and Characteristics
The crack propagation during the fracture process of the concrete specimens in this study was recorded using the DIC technique (Figures 9-11).The displacement jump map obtained by DIC was also adopted to reveal the development of crack characteristics (COD and ll) (Figures 12-14).The calculation method is described in Refs.[39,40].The crack characteristics were negligible during the early loading stage.

Crack Propagation and Characteristics
The crack propagation during the fracture process of the concrete specimens in this study was recorded using the DIC technique (Figures 9-11).The displacement jump map obtained by DIC was also adopted to reveal the development of crack characteristics (COD and ll) (Figures 12-14).The calculation method is described in Refs.[39,40].The crack characteristics were negligible during the early loading stage.

Crack propagation pattern;
The strain distributions of the specimens during the tests are shown in Figures 9-11.The initial cracking of the beam appeared on the tip of the notch when the vertical load (P) reached approximately 80% of the peak load (Pmax), and the fracture process zone (FPZ) of the specimen gradually increased as P increased, particularly when P decreased to approximately 80% of Pmax.When P decreased to 60% of Pmax, the FPZ expanded rapidly, and permanent cracks were formed which is in accordance with the observed failure pattern of the specimen (Section 3.1.1).

Crack characteristics.
DIC accurately captured the development of ll and COD during the fracture failure process (Figure 12).It can be observed that ll evidently changes with variations in the concrete mix components.When P reached 60% of Pmax, the ll values of SVSAC-0.3 and VSAC-0.3 were 2.64 mm and 5.91 mm, respectively, while the ll of OC-0.3 was negligible.The cracks in the specimen appeared earlier after adopting volcanic scoria, owing to the lightweight and porous structure of VSCA.When P approached Pmax, the CTOD values (COD at M0N0, Figure 13) of OC-0.3, SVSAC-0.3, and VSAC-0.3 were 0.041, 0.043, and 0.044 mm, respectively.However, the CTOD of OC-0.3 was 19.17% and 19.66% greater than those of VSAC-0.3 and SVSAC-0.3 when P decreased to 30% of Pmax, respectively (Figure 14).In addition, the ll value of

Physical Properties of SVSAC
The physical properties of concrete were obtained based on standard codes [41,42].The cubic compressive strength (fcu) of OC and VSAC was 38.3 MPa and 37.5 MPa, respectively (Table 4), which meets the requirements of this study.However, the splitting tensile and prismatic compressive strengths (fc and ft) of SVSAC increased by 12.04% and 17.31%, respectively, compared to those of OC, even under a similar fcu.The high mechanical interlock between VSCA and cement paste could inhibit the development of microcracks

Physical Properties of SVSAC
The physical properties of concrete were obtained based on standard codes [41,42].The cubic compressive strength (fcu) of OC and VSAC was 38.3 MPa and 37.5 MPa, respectively (Table 4), which meets the requirements of this study.However, the splitting tensile and prismatic compressive strengths (fc and ft) of SVSAC increased by 12.04% and 17.31%, respectively, compared to those of OC, even under a similar fcu.The high mechanical interlock between VSCA and cement paste could inhibit the development of microcracks

Crack propagation pattern;
The strain distributions of the specimens during the tests are shown in Figures 9-11.The initial cracking of the beam appeared on the tip of the notch when the vertical load (P) reached approximately 80% of the peak load (P max ), and the fracture process zone (FPZ) of the specimen gradually increased as P increased, particularly when P decreased to approximately 80% of P max .When P decreased to 60% of P max , the FPZ expanded rapidly, and permanent cracks were formed which is in accordance with the observed failure pattern of the specimen (Section 3.1.1).
DIC accurately captured the development of l l and COD during the fracture failure process (Figure 12).It can be observed that l l evidently changes with variations in the concrete mix components.When P reached 60% of P max , the l l values of SVSAC-0.3 and VSAC-0.3 were 2.64 mm and 5.91 mm, respectively, while the l l of OC-0.3 was negligible.The cracks in the specimen appeared earlier after adopting volcanic scoria, owing to the lightweight and porous structure of VSCA.
When P approached P max , the CTOD values (COD at M 0 N 0 , Figure 13) of OC-0.3, SVSAC-0.3, and VSAC-0.3 were 0.041, 0.043, and 0.044 mm, respectively.However, the CTOD of OC-0.3 was 19.17% and 19.66% greater than those of VSAC-0.3 and SVSAC-0.3 when P decreased to 30% of P max , respectively (Figure 14).In addition, the l l value of SVSAC-0.3 was 28.32% greater than that of OC-0.3, whereas the l l of VSAC-0.3 increased by 41.26% compared with that of SVSAC-0.3, revealing that the negative effect of VSCA on the cracking of concrete was reduced by SW and SS.This is because the Cl − in the SS and SW reacts with cement and yields Friedel's salt, which fills the internal pores and improves the microstructure of the concrete (Figure 15).After the peak point, cracking of the specimen developed rapidly, and the difference between the l l value of SVSAC-0.3 and that of VSAC-0.3 became minor (5.01%) when P decreased to 60% of P max .The influences of SS and SW on the l l value of SVSAC decreased at the final stage of loading owing to the failure of the microstructure of the concrete.

Physical Properties of SVSAC
The physical properties of concrete were obtained based on standard codes [41,42].The cubic compressive strength (fcu) of OC and VSAC was 38.3 MPa and 37.5 MPa, respectively (Table 4), which meets the requirements of this study.However, the splitting tensile and prismatic compressive strengths (fc and ft) of SVSAC increased by 12.04% and 17.31%, respectively, compared to those of OC, even under a similar fcu.The high mechanical interlock between VSCA and cement paste could inhibit the development of microcracks

Physical Properties of SVSAC
The physical properties of concrete were obtained based on standard codes [41,42].The cubic compressive strength (f cu ) of OC and VSAC was 38.3 MPa and 37.5 MPa, respectively (Table 4), which meets the requirements of this study.However, the splitting tensile and prismatic compressive strengths (f c and f t ) of SVSAC increased by 12.04% and 17.31%, respectively, compared to those of OC, even under a similar f cu .The high mechanical interlock between VSCA and cement paste could inhibit the development of microcracks and cause a higher f t .Compared to the elastic modulus (E c ) and apparent density (ρ d ) values of OC, those of SVSAC decreased by 29.34% and 16.85%, respectively, owing to the lightweight and porous structure of scoria aggregates.

Concrete
Type The crack initiation load (P ini ) and P max of the SVSAC were determined using the strain gauge method [43].Compared to the P ini of OC, that of the specimen adopting VSCA was reduced by 10.94% on average (Table 4).However, SW and SS can decrease the negative effects of the VSCA on the initial cracking of concrete.The results indicated that the P ini of SVSAC specimens was 4.98% higher than that of VSAC.The specific reasons are as follows: first, the porous structure and inferior properties of VSCA (i.e., modulus and strength) could not effectively inhibit the initiation of cracks, causing a lower P ini ; second, the high Cl − content promoted the hydration of cement and obtained more Friedel's salts, resulting in the dense microstructure of concrete and improvements in the P ini [44].
The P ini of SVSAC generally decreased with increasing notch-to-depth ratio (Figure 16a).It was obtained that the P ini of SVSAC-0.2 was 36% and 90% higher than those of SVSAC-0.3 and SVSAC-0.4,respectively.The SW, SS, and VSCA changed the influence of a 0 /h on P ini .Compared to SVSAC, the P ini of VSAC-0.2 was 36.29% and 91.67% greater than those of VSAC-0.3 and VSAC-0.4,respectively, and the effect of a 0 /h on P ini was reduced.

Pini
The crack initiation load (Pini) and Pmax of the SVSAC were determined using the strain gauge method [43].Compared to the Pini of OC, that of the specimen adopting VSCA was reduced by 10.94% on average (Table 4).However, SW and SS can decrease the negative effects of the VSCA on the initial cracking of concrete.The results indicated that the Pini of SVSAC specimens was 4.98% higher than that of VSAC.The specific reasons are as follows: first, the porous structure and inferior properties of VSCA (i.e., modulus and strength) could not effectively inhibit the initiation of cracks, causing a lower Pini; second, the high Cl − content promoted the hydration of cement and obtained more Friedel's salts, resulting in the dense microstructure of concrete and improvements in the Pini [44].
The Pini of SVSAC generally decreased with increasing notch-to-depth ratio (Figure 16a).It was obtained that the Pini of SVSAC-0.2 was 36% and 90% higher than those of SVSAC-0.3 and SVSAC-0.4,respectively.The SW, SS, and VSCA changed the influence of a0/h on Pini.Compared to SVSAC, the Pini of VSAC-0.2 was 36.29% and 91.67% greater than those of VSAC-0.3 and VSAC-0.4,respectively, and the effect of a0/h on Pini was reduced.

P max
The P max of SVSAC decreases with increasing a 0 /h (Table 4, Figure 16b).The P max of SVSAC-0.2 was 23.14% and 64.50% higher than those of SVSAC-0.3 and SVSAC-0.4,respectively.Furthermore, P max changed with variations in the concrete mix components.It was found that the P max of the VSCA specimen decreased by 9.47% on average compared with that of OC; however, the Cl − in SW and SS can hydrate with cement and improve the microstructure of concrete, causing the P max of SVSAC to be 13.47% greater than that of VSAC.

P-CMOD and P-CTOD Curves
The P-CMOD and P-CTOD curves are critical for determining the fracture properties of concrete (e.g., P ini , P max , and σ-CTOD relations).The P-CMOD and P-CTOD curves of the SVSAC specimens are shown in Figure 17 and can be divided into the initial linear ascending, crack propagation, and fracture failure sections.No visible cracks appeared in the SVSAC-notched beams when the curves were initially in the linearly ascending stage.Microcracks appeared at the notch tips, and the relationship between P and CMOD (CTOD) varied when P reached approximately P ini .In general, P increases nonlinearly with increasing CMOD (CTOD) during crack propagation.After P max , P declined dramatically and the CMOD (CTOD) continued to increase, indicating that the curves were in the fracture failure stage.Generally, the shape of the curve of SVSAC was similar to that of the curve of OC; however, several differences could be obtained.The mix components changed the development of P-CMOD and P-CTOD in concrete.Compared with OC, the decline in the P of the notched beams adopting VSCA became more rapid after the peak point, indicating the brittleness of SVSAC and VSAC (Figures 17-19).
ically and the CMOD (CTOD) continued to increase, indicating that the curves were in the fracture failure stage.Generally, the shape of the curve of SVSAC was similar to that of the curve of OC; however, several differences could be obtained.The mix components changed the development of P-CMOD and P-CTOD in concrete.Compared with OC, the decline in the P of the notched beams adopting VSCA became more rapid after the peak point, indicating the brittleness of SVSAC and VSAC (Figures 17-19).The energy required for the initiation of concrete cracks per unit area is denoted as the fracture energy (Gf), which reflects the energy dissipation during crack propagation.According to RILEM50-FMC [45,46] and Hillerborg et al. [47], the Gf of SVSAC can be obtained by P-δ and Equation (1).
( ) W0 represents the enclosed area below the measured P-CMOD curve, Pw is the selfweight of the beam, δ0 is the value of δ at P = 0, and t and h are the width and height of the concrete specimens, respectively.
The results revealed that the Gf of concrete with VSCA was inferior to that of OC under the same concrete strength grade (Figure 21).Compared to OC, the Gf of SVSAC and VSAC decreased by 32.59% and 37.27%, respectively.The energy dissipation capacity of concrete was significantly reduced after using VSCA, owing to the brittle nature of VSCA and low crack openings, which require less energy for crack propagation.However, SW and SS improved the Gf of concrete.The fracture energy of SVSAC increased by 7.47% compared with that of VSAC.The higher the Cl − content, the denser the concrete microstructure (Figure 22), the lower the crack propagation, and the greater the Gf of the concrete.The energy required for the initiation of concrete cracks per unit area is denoted as the fracture energy (G f ), which reflects the energy dissipation during crack propagation.According to RILEM50-FMC [45,46] and Hillerborg et al. [47], the G f of SVSAC can be obtained by P-δ and Equation (1).
W 0 represents the enclosed area below the measured P-CMOD curve, P w is the selfweight of the beam, δ 0 is the value of δ at P = 0, and t and h are the width and height of the concrete specimens, respectively.
The results revealed that the G f of concrete with VSCA was inferior to that of OC under the same concrete strength grade (Figure 21).Compared to OC, the G f of SVSAC and VSAC decreased by 32.59% and 37.27%, respectively.The energy dissipation capacity of concrete was significantly reduced after using VSCA, owing to the brittle nature of VSCA and low crack openings, which require less energy for crack propagation.However, SW and SS improved the G f of concrete.The fracture energy of SVSAC increased by 7.47% compared with that of VSAC.The higher the Cl − content, the denser the concrete microstructure (Figure 22), the lower the crack propagation, and the greater the G f of the concrete.
G f decreases with increasing a 0 /h.The G f of OC-0.2 was 17.35% and 32.11% higher than those of OC-0.3 and OC-0.4,respectively.Furthermore, VSCA enhanced the effect of a 0 /h on G f , and the G f of SVSAC-0.2 was 27.9% and 36.7% higher than those of SVSAC-0.3 and SVSAC-0.4,respectively.
VSCA and low crack openings, which require less energy for crack propagation.H SW and SS improved the Gf of concrete.The fracture energy of SVSAC increased b compared with that of VSAC.The higher the Cl − content, the denser the concret structure (Figure 22), the lower the crack propagation, and the greater the Gf of crete.Gf decreases with increasing a0/h.The Gf of OC-0.2 was 17.35% and 32.11% higher than those of OC-0.3 and OC-0.4,respectively.Furthermore, VSCA enhanced the effect of a0/h on Gf, and the Gf of SVSAC-0.2 was 27.9% and 36.7% higher than those of SVSAC-0.3 and SVSAC-0.4,respectively.

Characteristic Length
The characteristic length (Lch) proposed by Hillerborg et al. [47] was adopted to reflect the brittleness of concrete, as expressed in Equation (2).
Ec and ft denote the elastic modulus and splitting tensile strength of concrete, respectively.
The effects of a0/h and the concrete mix components on Lch (Figure 23) were similar to those of a0/h and the mix components on Gf.Generally, the Lch values of SVSAC and VSAC were, on average, 59.49% and 61.28% lower than those of OC, respectively, which indicated the brittleness of concrete containing VSCA.The Lch of the VSAC specimens was improved using SW and SS.It was found that the microstructure of the concrete was enhanced because the ions in the SS and SR were involved in the hydration reaction of the cement and the formation of salts, such as Friedel's filling of the voids in the VSCA.

Characteristic Length
The characteristic length (L ch ) proposed by Hillerborg et al. [47] was adopted to reflect the brittleness of concrete, as expressed in Equation ( 2).
E c and f t denote the elastic modulus and splitting tensile strength of concrete, respectively.The effects of a 0 /h and the concrete mix components on L ch (Figure 23) were similar to those of a 0 /h and the mix components on G f .Generally, the L ch values of SVSAC and VSAC were, on average, 59.49% and 61.28% lower than those of OC, respectively, which indicated the brittleness of concrete containing VSCA.The L ch of the VSAC specimens was improved using SW and SS.It was found that the microstructure of the concrete was enhanced because the ions in the SS and SR were involved in the hydration reaction of the cement and the formation of salts, such as Friedel's filling of the voids in the VSCA.

Double-K Fracture Parameters and Tension-Softening (σ-CTOD) Relations
Based on the above analyses, the fracture performance of SVSAC changed w ations in the concrete mix components and a0/h.Thus, the typical fracture propert as crack initiation and instability were evaluated by using the double-K fracture to and tension-softening relations (σ-CTOD) in detail.3) and ( 4)): values can be determined by Eq ( 5)-( 8): The L ch of SVSAC decreased and exhibited greater brittleness as a 0 /h increased.The results indicated that the L ch of SVSAC-0.2 increased by 40.56% and 63.48% compared to those of SVSAC-0.3 and SVSAC-0.4,respectively, revealing the rapid propagation of cracks and the high brittleness of concrete with a high initial crack length.

Double-K Fracture Parameters and Tension-Softening (σ-CTOD) Relations
Based on the above analyses, the fracture performance of SVSAC changed with variations in the concrete mix components and a 0 /h.Thus, the typical fracture properties such as crack initiation and instability were evaluated by using the double-K fracture toughness and tension-softening relations (σ-CTOD) in detail.Determination of fracture toughness; K ini IC and K un IC have always been employed to describe the crack initiation and instability of concrete based on Xu et al. [48,49].K ini IC represents the ability of concrete to inhibit cracks, and K un IC denotes the capacity of concrete to maintain the stable propagation of cracks.Generally, cracks could not develop when the stress intensity factor (K) was less than K ini IC (K < K ini IC ); cracks propagated stably when K ini IC < K < K un IC ; and cracks developed dramatically when K > K un IC .K ini IC and K un IC are expressed as (Equations ( 3) and ( 4)): where t, h, m, and S represent the thickness, height, self-weight, and span of the beam, respectively, g = 9.8 m/s 2 .The f (α 0 ) and f (α c ) values can be determined by Equations ( 5)-( 8): , , where CMOD c is the critical crack opening displacement and c i denotes the initial slope of the P-CMOD curves.

σ-CTOD Relations
The σ-CTOD relation (tension-softening curve) represents the relation between the tensile stress σ and CTOD in the FPZ of concrete, which reveals the ability of the concrete cracking to transmit σ.
In general, it was difficult to directly obtain σ-CTOD relations through the three-point bending beam test due to the non-uniform distribution of the cohesive force and the COD However, the fracture toughness of the SVSAC specimens was higher than that of the VSAC specimens owing to the effects of SW and SS.Compared with VSAC, the K ini IC and K un IC of SVSAC increased by 3.03% and 25.74%, respectively.The high concentration of Cl − ions in SW and SS can improve the microstructure of the concrete.Additionally, the formation of salts, such as Friedel's salt, can fill the voids in very small capillary pores, enhancing the fracture toughness of the concrete.
(2) Effect of a 0 /h.The effect of a 0 /h on fracture toughness is negligible [49].The test results indicated that the K ini IC and K un IC values of SVSAC were approximately 0.88 and 1.79, respectively (Figure 24a,b).

σ-CTOD Relations
The σ-CTOD relation (tension-softening curve) represents the relation between the tensile stress σ and CTOD in the FPZ of concrete, which reveals the ability of the concrete cracking to transmit σ.
In general, it was difficult to directly obtain σ-CTOD relations through the threepoint bending beam test due to the non-uniform distribution of the cohesive force and the COD [50].Thus, the J-integral method combined with the P-CTOD curve was used to derive the tensile-softening behavior of the concrete [51].According to the analyses and results, the σ-CTOD relations of SVSAC are shown in Figure 25.
Materials 2024, 17, x FOR PEER REVIEW [50].Thus, the J-integral method combined with the P-CTOD curve was used to de tensile-softening behavior of the concrete [51].According to the analyses and res σ-CTOD relations of SVSAC are shown in Figure 25.Compared with OC, the σ-CTOD curves of specimens adopting VSCA declin suddenly.This indicated that σ transmitted by the cracking surface of SVSAC wa icantly inferior to OC under a similar crack width condition.It was also found th values of OC at CTOD = 20, 50, and 100 µm were 2.37, 1.59, and 0.65 MPa, resp however, those of SVSAC were 1.66, 0.72, and 0.27 MPa, respectively.This ca tributed to the inferior mechanical properties of VSCA (porosity and low streng destruction of the coarse aggregate. Furthermore, the σ-CTOD of SVSAC dropped relatively slowly in comparis VSAC.The σ values of SVSAC at CTOD = 20 and 50 µm were 44.35% and 38.46% than those of VSAC at the same CTOD.SW and SS could efficiently improve the of SVSAC cracking to bear and transmit σ.Finally, the effects of SW and SS on the σ relation became negligible when CTOD reached 100 µm (0.1 mm), and the σ v SVSAC and VSAC were 0.27 and 0.30 MPa, respectively.The coarse aggregate aff entire crack propagation process; however, SS and SW have a notable impact on t stages of crack propagation, and their effect becomes minor when the CTOD rea mm.

General Expression
The addition of SW, SS, and VSCA could cause changes in the shape of the σ curve of SVSAC based on the test results, which indicates a variation in the mecha fracture.Thus, theoretical models of tension-softening relationships considering pled effects of concrete mix components need to be established to describe thes tions.Based on the experimental results and Ref. [52], the analytical expression o CTOD relations of SVSAC was obtained through Matlab (Matlab 24.1.0.(R2024a))analysis, as shown in Equation (9).Compared with OC, the σ-CTOD curves of specimens adopting VSCA declined more suddenly.This indicated that σ transmitted by the cracking surface of SVSAC was significantly inferior to OC under a similar crack width condition.It was also found that the σ values of OC at CTOD = 20, 50, and 100 µm were 2.37, 1.59, and 0.65 MPa, respectively; however, those of SVSAC were 1.66, 0.72, and 0.27 MPa, respectively.This can be attributed to the inferior mechanical properties of VSCA (porosity and low strength) and destruction of the coarse aggregate.
Furthermore, the σ-CTOD of SVSAC dropped relatively slowly in comparison with VSAC.The σ values of SVSAC at CTOD = 20 and 50 µm were 44.35% and 38.46% greater than those of VSAC at the same CTOD.SW and SS could efficiently improve the capacity of SVSAC cracking to bear and transmit σ.Finally, the effects of SW and SS on the σ-CTOD relation became negligible when CTOD reached 100 µm (0.1 mm), and the σ values of SVSAC and VSAC were 0.27 and 0.30 MPa, respectively.The coarse aggregate affects the entire crack propagation process; however, SS and SW have a notable impact on the early stages of crack propagation, and their effect becomes minor when the CTOD reaches 0.1 mm.

General Expression
The addition of SW, SS, and VSCA could cause changes in the shape of the σ-CTOD curve of SVSAC based on the test results, which indicates a variation in the mechanism of fracture.Thus, theoretical models of tension-softening relationships considering the coupled effects of concrete mix components need to be established to describe these variations.Based on the experimental results and Ref. [52], the analytical expression of the σ-CTOD relations of SVSAC was obtained through Matlab (Matlab 24.1.0.2508561 (R2024a))analysis, as shown in Equation (9).

Critical Parameters
The factors in Equation ( 9), a and b, significantly affect the characteristics of the tensionsoftening curve.The a and b in Equation ( 9) are critical parameters considering the effects of the mix components, and they can be derived through the analysis of the experimental data using a numerical regression analysis program coded in Matlab software (Equations ( 10) and ( 11)).
A comparison between the experimental and calculated curves is shown in Figure 26.The differences were acceptable, and the ability of the SVSAC cracking to transmit σ was reasonably predicted by the analytical model.The obtained curves are in good agreement with the real curves.
Materials 2024, 17, x FOR PEER REVIEW experimental data using a numerical regression analysis program coded in Matl ware (Equations ( 10) and ( 11)).

Numerical Simulation Analyses of Fracture
Nonlinear finite element (FE) analyses of SVSAC fracture were underta ABAQUS (Abaqus 6.14) software, and changes in the fracture mechanism and ma chanical properties of SVSAC under various conditions were systematically studi

FE Types and Material Properties
The FE element of SVSAC adopted a general-purpose linear solid brick C3D8R with reduced integration, which could properly describe the plastic proper damage evolution of materials.The advantage of using C3D8R for concrete mod time-saving and an acceptable results' accuracy.
Furthermore, the element of the loading steel plate of the three-point bendin was C3D8.
In general, ABAQUS software adopted three different constitutive models to d the mechanical properties and mechanism of concrete, i.e., the smeared crack mod aged plasticity model, and brittle cracking model.Based on the fracture test, th cracking model was used in this study owing to it being the most accurate in appl where brittle behavior dominates.Thus, this model was combined with the sugges

Numerical Simulation Analyses of Fracture
Nonlinear finite element (FE) analyses of SVSAC fracture were undertaken by ABAQUS (Abaqus 6.14) software, and changes in the fracture mechanism and macro-mechanical properties of SVSAC under various conditions were systematically studied.

FE Types and Material Properties
The FE element of SVSAC adopted a general-purpose linear solid brick element C3D8R with reduced integration, which could properly describe the plastic properties and damage evolution of materials.The advantage of using C3D8R for concrete modeling is time-saving and an acceptable results' accuracy.
Furthermore, the element of the loading steel plate of the three-point bending beam was C3D8.
In general, ABAQUS software adopted three different constitutive models to describe the mechanical properties and mechanism of concrete, i.e., the smeared crack model, damaged plasticity model, and brittle cracking model.Based on the fracture test, the brittle cracking model was used in this study owing to it being the most accurate in applications where brittle behavior dominates.Thus, this model was combined with the suggested tension-softening relation of SVSAC (Equation ( 9)) to investigate the variations in the fracture mechanism and macro-properties of specimens under different conditions.
The elasto-plastic constitutive model was proposed for the steel plate, and the related stress-strain curve refers to Ref. [53].

Establishment of FE Model of Fracture Specimen
The establishment of the nonlinear FE model of the SVSAC three-point bending specimen mainly consisted of two steps.First, the geometric entities of the beam and loading plate were built (Figure 27a).Second, the element type, material properties, and constitutive model were assigned, and the entities were meshed (Figure 27b).Third, the boundary of the beam (two ends) was fixed and the displacement loading program was adopted according to the actual test.Finally, numerical simulations of the specimen were performed under different conditions.The establishment of the nonlinear FE model of the SVSAC three-point bending specimen mainly consisted of two steps.First, the geometric entities of the beam and loading plate were built (Figure 27a).Second, the element type, material properties, and constitutive model were assigned, and the entities were meshed (Figure 27b).Third, the boundary of the beam (two ends) was fixed and the displacement loading program was adopted according to the actual test.Finally, numerical simulations of the specimen were performed under different conditions.
It should be noted that the proper size of elements was determined after the preliminary studies.The element size of concrete at the tip of beam notch kept 0.5 mm (height) × 3 mm (length) × 3 mm (width), while the size of the other elements was approximately 3-30 mm.

Validity of FE Model
A comparison between the numerical results and test results is shown in Figures 28  and 29.It was obtained that the model predicted the fracture response of SVSAC with acceptable accuracy.The simulated failure process and P-CMOD curves of SVSAC were in line with the test data.Thus, the suggested numerical model and σ-CTOD relation (Equation ( 9)) were adopted to study the fracture mechanism and macro-mechanical properties of SVSAC under critical variables (e.g., sizes of specimen).It should be noted that the proper size of elements was determined after the preliminary studies.The element size of concrete at the tip of beam notch kept 0.5 mm (height) × 3 mm (length) × 3 mm (width), while the size of the other elements was approximately 3-30 mm.

Validity of FE Model
A comparison between the numerical results and test results is shown in Figures 28  and 29.It was obtained that the model predicted the fracture response of SVSAC with acceptable accuracy.The simulated failure process and P-CMOD curves of SVSAC were in line with the test data.Thus, the suggested numerical model and σ-CTOD relation (Equation ( 9)) were adopted to study the fracture mechanism and macro-mechanical properties of SVSAC under critical variables (e.g., sizes of specimen).The establishment of the nonlinear FE model of the SVSAC three-point bending specimen mainly consisted of two steps.First, the geometric entities of the beam and loading plate were built (Figure 27a).Second, the element type, material properties, and constitutive model were assigned, and the entities were meshed (Figure 27b).Third, the boundary of the beam (two ends) was fixed and the displacement loading program was adopted according to the actual test.Finally, numerical simulations of the specimen were performed under different conditions.
It should be noted that the proper size of elements was determined after the preliminary studies.The element size of concrete at the tip of beam notch kept 0.5 mm (height) × 3 mm (length) × 3 mm (width), while the size of the other elements was approximately 3-30 mm.

Validity of FE Model
A comparison between the numerical results and test results is shown in Figures 28  and 29.It was obtained that the model predicted the fracture response of SVSAC with acceptable accuracy.The simulated failure process and P-CMOD curves of SVSAC were in line with the test data.Thus, the suggested numerical model and σ-CTOD relation (Equation ( 9)) were adopted to study the fracture mechanism and macro-mechanical properties of SVSAC under critical variables (e.g., sizes of specimen).

Numerical Results of SVSAC
Generally, several critical fracture parameters of concrete greatly changed w ation in the size of the specimen [54,55], particular its fracture toughness ( ini IC K an and P-CMOD curve.However, it is difficult to obtain the independent effect on ture of concrete experimentally.Thus, numerical simulations were undertaken changes in fracture properties was obtained. Four different heights (H = 150, 200, 250, and 300 mm), lengths (L = 900, 119 and 1800 mm), and widths (W = 80, 100, 120, and 140 mm) of the SVSAC beam w sidered in the FE analyses, and the variations in Pmax, ini IC K , and n IC u K are listed in It was observed that Pmax increased with increasing H and W while decreasing higher (lower) the H and W (L), the greater the stiffness of the specimen, and the the Pmax.Furthermore, the fracture toughness ( ini IC K and n IC u K ) was obviously im through increasing L and decreasing H (Figure 30).The test results indicated that and n IC u K of specimens with 300 mm H were 28% and 35% inferior compared wi of specimens with 150 mm H, respectively.This phenomenon can be attribute toughness of the beam being significantly reduced by an improvement in structu ness [56].
The characteristics of the P-CMOD curves of SVSAC also changed with a var the size of the specimen (Figure 31).It was obtained that the descending portio curve became steep after increasing H and decreasing L, which caused inferior d bility and unstable fracture toughness ( n IC u K ) of SVSAC.Furthermore, the critical (CMODc) was also improved through enhancing the size of the specimen.Gener CMODc of specimens with 300 mm H was 35.9% greater compared with that of sp with 150 mm H.

Numerical Results of SVSAC
Generally, several critical fracture parameters of concrete greatly changed with variation in the size of the specimen [54,55], particular its fracture toughness (K ini IC and K un IC ) and P-CMOD curve.However, it is difficult to obtain the independent effect on the fracture of concrete experimentally.Thus, numerical simulations were undertaken and the changes in fracture properties was obtained.
Four different heights (H = 150, 200, 250, and 300 mm), lengths (L = 900, 1190, 1500, and 1800 mm), and widths (W = 80, 100, 120, and 140 mm) of the SVSAC beam were considered in the FE analyses, and the variations in P max , K ini IC , and K un IC are listed in Table 5.It was observed that P max increased with increasing H and W while decreasing L. The higher (lower) the H and W (L), the greater the stiffness of the specimen, and the greater the P max .Furthermore, the fracture toughness (K ini IC and K un IC ) was obviously improved through increasing L and decreasing H (Figure 30).The test results indicated that the K ini IC and K un IC of specimens with 300 mm H were 28% and 35% inferior compared with those of specimens with 150 mm H, respectively.This phenomenon can be attributed to the toughness of the beam being significantly reduced by an improvement in structure stiffness [56].The characteristics of the P-CMOD curves of SVSAC also changed with a variation in the size of the specimen (Figure 31).It was obtained that the descending portion of the curve became steep after increasing H and decreasing L, which caused inferior deformability and unstable fracture toughness (K un IC ) of SVSAC.Furthermore, the critical CMOD (CMOD c ) was also improved through enhancing the size of the specimen.Generally, the CMOD c of specimens with 300 mm H was 35.9% greater compared with that of specimens with 150 mm H.

Analytical Model of Fracture Toughness Considering Size Effect and Mix Component
Based on the simulation results and the experimental data, the fracture toughness (K ini IC and K un IC ) of SVSAC was significantly affected by the concrete mix components and specimen size.However, few studies have focused on this field, and few analytical models have been used to characterize the changes in fracture toughness caused by mix components and size components.
Thus, according to Refs.[32,[57][58][59][60][61] and the results, a theoretical model was developed to consider the effects of SW, SS, VSCA, and specimen size.Matlab software was also used to code a numerical program for the regression analysis, which was adopted to investigate the experimental and numerical data and obtain a specific formula.The analytical expressions for K ini IC and K un IC are expressed as Equations ( 12) and ( 13):

Figure 12 .
Figure 12.The crack propagation length during different loading steps.

KK
have always been employed to describe the crack initiation an bility of concrete based on Xu et al. [48,49].ini IC K represents the ability of concre hibit cracks, and n IC u K denotes the capacity of concrete to maintain the stable prop of cracks.Generally, cracks could not develop when the stress intensity factor (K) than ini IC K (K < ini IC K ); cracks propagated stably when ini IC are expressed as (Equations ( , where t, h, m, and S represent the thickness, height, self-weight, and span of th respectively, g = 9.8 m/s 2 .The ( )

Figure 23 .
Figure 23.L ch with different a 0 /h.

Figure 24 .
Figure 24.The variation in fracture toughness: (a) ini IC K ; (b) n IC u K .
the experimental and calculated curves is shown in Fi The differences were acceptable, and the ability of the SVSAC cracking to transm reasonably predicted by the analytical model.The obtained curves are in good agr with the real curves.

Figure 26 .
Figure 26.Comparison of softening curves between test and calculation.

Figure 27 .
Figure 27.FE model of specimen: (a) Geometric entities of specimen; (b) FE mesh of specimen.

Figure 27 .
Figure 27.FE model of specimen: (a) Geometric entities of specimen; (b) FE mesh of specimen.

Figure 27 .
Figure 27.FE model of specimen: (a) Geometric entities of specimen; (b) FE mesh of specimen.

Figure 29 .
Figure 29.P-CMOD curves of SVSAC from experiment and simulation.

Table 1 .
Properties of the coarse and fine aggregates.

Table 1 .
Properties of the coarse and fine aggregates.

Table 1 .
Properties of the coarse and fine aggregates.

Table 3 .
Parameters of the specimen.

Table 3 .
Parameters of the specimen.

Table 4 .
Physical properties of concrete and fracture parameters.

Table 5 .
Fracture behaviors of SVSAC under different size conditions.

Table 5 .
Fracture behaviors of SVSAC under different size conditions.
5.3.Analytical Model of Fracture Toughness Considering Size Effect and Mix ComponentBased on the simulation results and the experimental data, the fracture toughness ini IC K and n IC u K ) of SVSAC was significantly affected by the concrete mix components and specimen size.However, few studies have focused on this field, and few analytical model

Table 5 .
Fracture behaviors of SVSAC under different size conditions.